Lipschitz stability of solutions to parametric optimal control problems for parabolic equations.
Littlewood-Paley a priori estimates for parabolic equations with sub-Dini continuous coefficients
L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type
Error estimates in L∞(0,T;L2(Ω)), L∞(0,T;L2(Ω)2), L∞(0,T;L∞(Ω)), L∞(0,T;L∞(Ω)2), Ω in , are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation based on the Raviart-Thomas space Vh x Wh ⊂ H(div;Ω) x L2(Ω). Optimal order estimates are obtained for the approximation of u,ut in L∞(0,T;L2(Ω)) and the associated velocity p in L∞(0,T;L2(Ω)2), divp in L∞(0,T;L2(Ω)). Quasi-optimal order estimates are obtained for the approximation...
Local attractivity in nonautonomous semilinear evolution equations
We study the local attractivity of mild solutions of equations in the form u’(t) = A(t)u(t) + f (t, u(t)), where A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at infinity...
Local boundedness for solutions of doubly nonlinear parabolic equations.
Local boundedness of weak solutions for nonlinear parabolic problem with -growth.
Local Collapses in the Truscott-Brindley Model
Relaxation oscillations are limit cycles with two clearly different time scales. In this article the spatio-temporal dynamics of a standard prey-predator system in the parameter region of relaxation oscillation is investigated. Both prey and predator population are distributed irregularly at a relatively high average level between a maximal and a minimal value. However, the slowly developing complex pattern exhibits a feature of “inverse excitability”: Both populations show collapses which occur...
Local exact controllability of the age-dependent population dynamics with diffusion.
Local exact controllability of the diffusion equation in one dimension.
Local exact lagrangian controllability of the Burgers viscous equation
Local Existence and Regularity for a Class of Degenerate Parabolic Equations.
Local existence, uniqueness and regularity for a class of degenerate parabolic systems arising in biological models
Local one-dimensional scheme for the third boundary value problem for the heat equation.
Local solution for the Kadomtsev-Petviashvili equation with periodic conditions.
Local solution of parabolic equations with strongly increasing nonlinearity by the Rothe method
Local solvability of a constrained gradient system of total variation.
Local solvability of diagonal semilinear parabolic systems
Local stability of spike steady states in a simplified Gierer-Meinhardt system.
Localization and Blow-Up of Thermal Waves in Nonlinear Heat Conduction with Peaking.
Log-concavity in some parabolic problems.